If `a_1, a_2, a_3,...a_20` are A.M's inserted between 13 and 67 then the maximum value of the product `a_1 a_2 a_3...a_20 ` is

If a_1, a_2, a_3,...a_n are in A.P with common difference d !=0 then the value of sind(coseca_1 coseca_2 +cosec a_2 cosec a_3+...+cosec a_(n-1) cosec a_n) will be

If a_1+a_2+a_3+......+a_n=1 AA a_1 > 0, i=1,2,3,......,n, then find the maximum value of a_1 a_2 a_3 a_4 a_5......a_n.

Let a_1,a_2,a_3,... be in A.P. With a_6=2. Then the common difference of the A.P. Which maximises the product a_1a_4a_5 is :

If a_1, a_2, a_3..... a_n in R^+ and a_1.a_2.a_3.........a_n = 1, then minimum value of (1+a_1 + a_1^2) (1 + a_2 + a_2^2)(1 + a_3 + a_3^2)........(1+ a_n + a_n^2) is equal to :-

If a_1,a_2,a_3,.....,a_n are in AP where a_i ne kpi for all i , prove that cosec a_1* cosec a_2+ cosec a_2* cosec a_3+...+ cosec a_(n-1)* cosec a_n=(cota_1-cota_n)/(sin(a_2-a_1)) .